Problem: Rewrite as a simplified fraction. ${2.8\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 286.6666...\\ 10x &= 28.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 258}$ ${x = \dfrac{258}{90}} $ ${x = \dfrac{43}{15}} \text{or} {2 \dfrac{13}{15}}$